sigex.acf: Compute the autocovariance function of a differenced latent...
In jlivsey/sigex: Ecce Signum: Multivariate Signal Extraction

sigex.acf

R Documentation

Compute the autocovariance function of a differenced latent component

Description

Background: A sigex model consists of process x = sum y, for stochastic components y. Each component process y_t is either stationary or is reduced to stationarity by application of a differencing polynomial delta(B), i.e. w_t = delta(B) y_t is stationary. We have a model for each w_t process, and can compute its autocovariance function (acf), and denote its autocovariance generating function (acgf) via gamma_w (B). Sometimes we may over-difference, which means applying a differencing polynomial eta(B) that contains delta(B) as a factor: eta(B) = delta(B)*nu(B). Then eta(B) y_t = nu(B) w_t, and the corresponding acgf is nu(B) * nu(B^-1) * gamma_w (B).

Usage

sigex.acf(L.par, D.par, mdl, comp, mdlPar, delta, maxlag, freqdom = FALSE)

Arguments

`L.par`	Unit lower triangular matrix in GCD of the component's white noise covariance matrix.
`D.par`	Vector of logged entries of diagonal matrix in GCD of the component's white noise covariance matrix.
`mdl`	The specified sigex model, a list object
`comp`	Index of the latent component
`mdlPar`	This is the portion of param corresponding to mdl[[2]], cited as param[[3]]
`delta`	Differencing polynomial (corresponds to eta(B) in Background) written in format c(delta0,delta1,...,deltad)
`maxlag`	Number of autocovariances required
`freqdom`	A flag, indicating whether frequency domain acf routine should be used.

Details

Notes: this function computes the over-differenced acgf, it is presumed that the given eta(B) contains the needed delta(B) for that particular component. Conventions: ARMA and VAR models use minus convention for (V)AR polynomials, and additive convention for (V)MA polynomials. SARMA and SVARMA use minus convention for all polynomials.